The rest of the paper is organized as follows. Section 2 sets out
the notation, definition and smoothing properties necessary to give
our main results in section 3. Section 4 extends the convexification
of non convex domain of [1]} for strongly convex
outside the ball to non-strongly convex outside the ball, and employs
this outcome in combination with regularization to obtain convergence
in KL divergence for potentials which satisfy log Sobolev, Talagrand,
Poincaré inequalities, or non-strongly convex at infinity while Section
5 presents our conclusions.
